Cremona's table of elliptic curves

1394 = 2 · 17 · 41

Field	Data	Notes
Atkin-Lehner	2+ 17+ 41+	Signs for the Atkin-Lehner involutions
Class	1394a	Isogeny class
Conductor	1394	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	994936832 = 211 · 172 · 412	Discriminant
Eigenvalues	2+  0  0  0  0  4 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-10937,442989]	[a1,a2,a3,a4,a6]
Generators	[65:27:1]	Generators of the group modulo torsion
j	144690722229371625/994936832	j-invariant
L	2.0309687002802	L(r)(E,1)/r!
Ω	1.3964967845884	Real period
R	1.4543310967084	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	11152k2 44608b2 12546m2 34850t2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1394a2

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	0	0	0	0	4	+	-6	0	6	4	-8	+	-8	-4	4	-4	0	-10	8	-6	-8	0	-6	14

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Quadratic twists for elliptic curve 1394a2

-4	8	-3	5	-7	17	41
11152k2	44608b2	12546m2	34850t2	68306j2	23698b2	57154d2

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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